On Edgeworth Expansions in Generalized Urn Models

On Generalized Pólya Urn Models

We study an urn model introduced in the paper of Chen and Wei [2], where at each discrete time step m balls are drawn at random from the urn containing colors white and black. Balls are added to the urn according to the inspected colors, generalizing the well known Pólya-Eggenberger urn model, case m = 1. We provide exact expressions for the expectation and the variance of the number of white b...

Edgeworth Expansions for Errors-in-Variables Models

Edgeworth expansions for sums of independent but not identically distributed multivariate random vectors are established. The results are applied to get valid Edgeworth expansions for estimates of regression parameters in linear errors-invariable models. The expansions for studentized versions are also developed. Further, Edgeworth expansions for the corresponding bootstrapped statistics are ob...

Rearranging Edgeworth- Cornish-Fisher Expansions

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of distribution and quantile functions, the procedure often delivers strikingly better approximations to the dist...

Generalized Urn Models of Evolutionary Processes

Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are: Under what conditions does a population exhibit growth? On the event of growth, at what rate does the population increase? What is the long term behavior of the distribution of genotypes? To address these questions, we associate a mean limit ...

Interpretation and Manipulation of Edgeworth Expansions